a)
a=5cm
[tex]V=a^3=(5cm)^3=125cm^3[/tex]
[tex]P=6a^2=6\cdot(5cm)^2=6\cdot25\,cm^2=150\ cm^2[/tex]
b) (czworościan foremny, bo inaczej jest za mało danych)
a = 8cm
[tex]V=\frac{a^3\sqrt2}{12}=\frac{8^3\sqrt2}{12}=\frac{64\cdot8\sqrt2}{12}=\frac{64\cdot2\sqrt2}{3}=\frac{128\sqrt2}{3}\ cm^3\\\\P_c=a^2\sqrt3=8^2\sqrt3=64\sqrt3\ cm^2[/tex]
c)
a=5m
b=4m
c=7m
V=abc = 5m·4m·7m = 140m³
Pc= 2ab+2bc+2ac = 2·5·4 + 2·4·7+2·5·7 = 40+56+70=166m²
d)
a=3cm
H=10cm
[tex]V=P_p\cdot H=a^2\cdot H = (3cm)^2\cdot 10cm=90\,cm^3\\\\P_c=2P_p+P_b=2a^2+4aH=2\cdot3^2+2\cdot3\cdot10=18+60=78\,cm^2[/tex]
a=5cm
H=10cm
[tex]V=P_p\cdot H=a^2\cdot H = (5cm)^2\cdot 10cm=250\,cm^3\\\\P_c=2P_p+P_b=2a^2+4aH=2\cdot5^2+2\cdot5\cdot10=50+100=150\,cm^2[/tex]
